The Emergence of Classicality via Decoherence Described by Lindblad Operators

Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for the quantum master equation. In both cases, the maximally predictive states ...

Quantum and classical systems evolving under the same formal Hamiltonian $H$ may exhibit dramatically different behavior after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classic...

In closed quantum systems, wavepackets can spread exponentially in time due to chaos, forming long-range superpositions in just seconds for ordinary macroscopic systems. A weakly coupled environment is conjectured to decohere the system and restore the quantum-classical correspondence while necessarily introducing diffusive noise -- but for what coupling strength, and under what conditions? For Markovian open systems with Hamiltonians of the form $H=p^2/2m + V(x)$ and linear ...

We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection einselection in a more general setting, we ...

Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered environment can drive the system toward exotic phases of matter or toward subspaces protected from noise. These cases often require the Lindbladian to have more than one steady state, and such Lindbladians are dissipativ...

Open quantum systems undergo decoherence, responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators, sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as function of time. This decay ...

The emergence of classical behaviour in quantum theory is often ascribed to the interaction of a quantum system with its environment, which can be interpreted as environmental monitoring of the system. As a result, off-diagonal elements of the density matrix of the system are damped in the basis of a preferred observable, often taken to be the position, leading to the phenomenon of decoherence. This effect can be modelled dynamically in terms of a Lindblad equation driven by ...

The aim of this paper is to review a new perspective about decoherence, according to which formalisms originally devised to deal just with closed or open systems can be subsumed under a closed-system approach that generalizes the traditional account of the phenomenon. This new viewpoint dissolves certain conceptual difficulties of the orthodox open-system approach but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decohere...

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytic...

Notions of robust and "classical" states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition of trace class operators. Using the predictability sieve proposed by Zurek, ``quasi-classical'' states are defined. A number of examples illustrating how the ``quasi-classical'' states correspond to classical points in phase space connected with the measuring apparatus are presented.